Question

Triangle XYZ is reflected over a horizontal line of reflection to create triangle X′Y′Z′ . What are the coordinates of vertex X′ ? (1 point) Responses
(−3,−9)
(−3,−7)
(3,−9)
(−2,−2)

Answer 1

To determine the coordinates of vertex \( X' \) after triangle \( XYZ \) is reflected over a horizontal line, we need to know the original coordinates of point \( X \) and the equation of the line of reflection.

Assuming point \( X \) has the coordinates \( (x, y) \) and the line of reflection is \( y = k \), then the y-coordinate of the reflected point \( X' \) can be calculated as follows:

1. **Find the distance from point \( X \) to the line of reflection**:
\[
\text{Distance} = y - k
\]
2. **Since the reflection will be at the same distance on the other side of the line**:
\[
y' = k - (y - k) = 2k - y
\]
3. **The x-coordinate remains unchanged**:
\[
x' = x
\]

Consequently, the coordinates of \( X' \) will be \( (x, 2k - y) \).

Without the specific coordinates for point \( X \) and the line of reflection, I cannot directly determine the coordinates of \( X' \) from the provided options. Could you please provide the coordinates of point \( X \) or additional information about the line of reflection?